Veranstaltungen
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- Mittwoch, 07.06.2023, 11:30 Uhr (WIAS-405-406)
- Seminar Interacting Random Systems
Günter Last, Karlsruher Institut für Technologie:
A Palm approach to tail processes and tail measures
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
Tail processes and tail measures are important concepts in the theory of regularly varying (heavy tailed) time series. In this talk we will show that these concepts are intimately related to Palm theory of stationary random measures. To motivate the topic, we start with providing some background on regularly varying time series. Then we shall introduce tail fields in an intrinsic way, namely as spectrally decomposable random fields satisfying a certain space shift formula. The index set is allowed to be a general locally compact Hausdorff Abelian group. The field may take its values in an Euclidean space or even in an arbitrary measurable cone, equipped with a pseudo norm. We characterize mass-stationarity of the exceedance random measure in terms of a suitable version of the classical Mecke equation. As a rule, the associated stationary measure is not finite. We shall show that it is homogeneous, that is a tail measure. Finally we will establish a spectral representation of stationary tail measures. The talk is based on our recent work arXiv:2112.15380.
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Seminar Interacting Random Systems (Hybrid Event)
Veranstalter
WIAS Berlin
- Dienstag, 06.06.2023, 15:00 Uhr (WIAS-405-406)
- Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Simon Breneis, WIAS Berlin:
American options under rough Heston (hybrid talk)
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
Abstrakt
The rough Heston model is a popular option pricing model in mathematical finance. However, due to the non-semimartingale and non-Markovian characteristics of its volatility process, simulations can be prohibitively expensive in practice. Building on previous works, we approximate the volatility process with an N-dimensional diffusion, yielding a Markovian approximation of the rough Heston model. Then, we introduce a weak discretization scheme to simulate paths of these Markovian approximations. Our numerical experiments show that these approximations converge at a second-order rate as the number of time steps approaches infinity. We leverage these approximations to price American options under the rough Heston model.
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Dieser Vortrag findet auch via Zoom statt: https://zoom.us/j/492088715
Veranstalter
WIAS Berlin